System approach to mathematical modeling of filtration consolidation

Abstract

Filtration consolidation is modeled taking into account salt saturation of soil and the nonisothermal and relaxation nature of the filtration process. A boundary-value problem for a soil mass consolidated on an impermeable bed is posed, its approximated solution is obtained, and the results of numerical experiments are presented.

Mathematical modeling of the filtration consolidation of water-saturated randomly inhomogeneous soil masses

“…Similarly to [4], to eliminate differential operations in x and y, we solve it by the integral-transforms method.…”

Mathematical modeling of filtration consolidation with salt transfer in a double-relaxation system

“…The function H x t 0 ( , ) can be found easily based on (19) in view of the boundary conditions Since the equation for determining H 0 corresponds to the case of classical filtration consolidation under conditions of the Darcy law and u 1 is a boundary layer function, we may conclude that the consolidation model under study for media with weakly pronounced relaxation properties of both filtration and deformation is close in a sense to the classical Terzaghi-Gersevanov consolidation model [1][2][3] generalized to the conditions of motion of saline solutions [5,6].…”

“…An analysis of the consolidation of bases of surface industrial and household sewage ponds is important because of environmental protection problems [4,5]. These sewage ponds are often filled with industrial waste products that are concentrated saline solutions; therefore, the dynamics of consolidation of bases of these sewage ponds cannot be analyzed using the classical theory of filtration consolidation, which is based on the assumption that the filtrate in the soil mass is pure water [1][2][3], and it is necessary to account for saline mass transfer during the filtration of a pore solution [4][5][6].…”

“…Applying the generalized mean-value theorem to the integral in (6) and approximating the resultant integral using a quadrature formula, for example, the trapezoid rule, we pass from the integro-differential equation (6) to the differential one…”

Generalized mathematical model of the dynamics of consolidation processes with relaxation

“…Some of the results of the research within the framework of this problem are elucidated in [1][2][3]. In constructing the mathematical models of consolidation in case of a complex internal structure of the solutions that fill sewage ponds, it is important to account for the relaxation properties of the filtration process [4], which causes the use of the dependences other than the classical Darcy law.…”